A Directed Acyclic Graph (DAG) of tasks with small communication delays has to be scheduled on the identical parallel processors of clusters connected by a hierarchical network. The number or processors and of clusters is not limited. Message contention has to be avoided. Task duplication is allowed. In this paper, we present a new polynomial algorithm that computes the earliest start dates of all tasks and spreads these tasks to use few processors per cluster, for a DAG with small communication delays. It also avoids message contention, and always delivers messages on time.